Exam 5: The Time Value of Money

Al Corbin is 25 years old today and wishes to accumulate enough money over the next 35 years to provide for a 20-year retirement annuity of $100,000 at the beginning of each year, starting with his 60th birthday. He can save $2,000 at the end of each of the next 10 years and $3,000 each year for the following 10 years. How much must he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return over the entire period will be 10%.

Explain the sinking fund problem.

The payment or receipt of a series of equal cash flows per period, at the end of each period, for a specified amount of time is called a(n) ____.

Columbia Bank & Trust has just given you a $20,000 term loan to pay for a new concrete mixer. The loan requires five equal annual end-of-the-year payments. If the loan provides the bank with a 12 percent return, what will be your annual payments?

Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to the maximum age of 80 and wants to be able to withdraw $25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore.

1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What effective annual interest rate is the bank charging you?

The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. What will be the outstanding balance after the third payment?

Which of the following is worth more?

Bill Swill decides to try his luck at Powerball where the projected winnings are $12,000,000. If he wins, he can choose the annuity option (to be paid over 20 years) or a lump sum settlement that he can invest at 8% interest. How much must the lump sum option be to make the lump sum option equal to the annuity option (rounded)?

What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly?

Using the "Rule of 72," about how long will it take a sum of money to double in value if the annual interest rate is 9 percent?

If the present value of a given sum is equal to its future value, then ____.

Your firm, New Sunrise, has just leased a $28,000 BMW for you. The lease requires six beginning-of-the-year payments that will fully amortize the cost of the car. What is the amount of the payments if the interest rate is 12 percent?

What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded monthly?

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest compounded annually, what is the value of the fund today?

If you invest $10,000 in a 4-year certificate of deposit (CD) paying 10 percent interest compounded annually, determine how much the CD will be worth at the end of 4 years.

The lease on a new office requires an immediate payment of $24,000 plus $24,000 per year at the end of each of the next 10 years. At a discount rate of 14 percent, what is the present value of this stream of lease payments?

Sherry Smart is buying a $350,000 home and will pay the mortgage monthly for 30 years. She has a good credit score and has qualified for a 5.125% loan interest. How much will she be paying monthly for the home?

Designs Now is opening a showcase office to display and sell its computer-designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows?

Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over the accumulation period, how much must she save per year (end of year) to have the $200,000?